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The Simple Chromatic Number of Oriented Graphs

✍ Scribed by Petra Smolikovaa


Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
202 KB
Volume
5
Category
Article
ISSN
1571-0653

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πŸ“œ SIMILAR VOLUMES


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We introduce in this paper the notion of the chromatic number of an oriented graph G (that is of an antisymmetric directed graph) defined as the minimum order of an oriented graph H such that G admits a homomorphism to H. We study the chromatic number of oriented k-trees and of oriented graphs with

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## Abstract Given a simple plane graph __G__, an edge‐face __k__‐coloring of __G__ is a function Ο• : __E__(__G__) βˆͺ __F__(G) →  {1,…,__k__} such that, for any two adjacent or incident elements __a__, __b__ ∈ __E__(__G__) βˆͺ __F__(__G__), Ο•(__a__) ≠ ϕ(__b__). Let Ο‡~e~(__G__), Ο‡~ef~(__G__), and Ξ”(__G_

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The oriented chromatic number Ο‡ o ( G) of an oriented graph G = (V, A) is the minimum number of vertices in an oriented graph H for which there exists a homomorphism of G to H. The oriented chromatic number Ο‡ o (G) of an undirected graph G is the maximum of the oriented chromatic numbers of all the

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## Abstract A homomorphism from an oriented graph __G__ to an oriented graph __H__ is a mapping $\varphi$ from the set of vertices of __G__ to the set of vertices of __H__ such that $\buildrel {\longrightarrow}\over {\varphi (u) \varphi (v)}$ is an arc in __H__ whenever $\buildrel {\longrightarrow}